Hyperbolic vectors are called gyrovectors. We show that the Bloch vector of quantum mechanics is a gyrovector. The Bures fidelity between two states of a qubit is generated by two Bloch vectors. Treating these as gyrovectors rather than vectors results in our novel expression for the Bures fidelity, expressed in terms of its two generating Bloch gyrovectors. Taming the Thomas precession of Einstein's special theory of relativity led to the advent of the theory of gyrogroups and gyrovector (...) spaces. Gyrovector spaces, in turn, form the setting for various models of the hyperbolic geometry of Bolyai and Lobachevski just as vector spaces form the setting for the standard model of Euclidean geometry. It is the recent advent of the theory of gyrogroups and gyrovector spaces that allows the Bures fidelity to be studied in its natural context, hyperbolic geometry, resulting in our new representation of the Bures fidelity, that reveals simplicity, elegance, and hyperbolic geometric significance. (shrink)

The connection between the Minkowskian geometry of the plane and its projective geometry is exemplified by the Einstein velocity addition theorem.

An homage to the men and women of science, and an exposition of Einstein's place in scientific history In this fascinating collection of articles and speeches, Albert Einstein reflects not only on the scientific method at work in his own theoretical discoveries, but also eloquently expresses a great appreciation for his scientific contemporaries and forefathers, including Johannes Kepler, Isaac Newton, James Clerk Maxwell, Max Planck, and Niels Bohr. While Einstein is renowned as one of the foremost innovators of modern (...) science, his discoveries uniquely his own, through his own words it becomes clear that he viewed himself as only the most recent in a long line of scientists driven to create new ways of understanding the world and to prove their scientific theories. Einstein's thoughtful examinations explain the "how" of scientific innovations both in his own theoretical work and in the scientific method established by those who came before him. This authorized Philosophical Library book features a new introduction by Neil Berger, PhD, and an illustrated biography of Albert Einstein, which includes rare photos and never-before-seen documents from the Albert Einstein Archives at the Hebrew University of Jerusalem. "What place does the theoretical physicist's picture of the world occupy among all these possible pictures? It demands the highest possible standard of rigorous precision in the description of relations, such as only the use of mathematical language can give" -Albert Einstein, "Principles of Research" Albert Einstein (1879-1955) was born in Germany and became an American citizen in 1934. A world-famous theoretical physicist, he was awarded the 1921 Nobel Prize for Physics and is renowned for his Theory of Relativity. In addition to his scientific work, Einstein was an influential humanist who spoke widely about politics, ethics, and social causes. After leaving Europe, Einstein taught at Princeton University. His theories were instrumental in shaping the atomic age. Neil Berger, an associate professor emeritus of mathematics, taught at the University of Illinois at Chicago in the Mathematics, Statistics, and Computer Science department from 1968 until his retirement in 2001. He was the recipient of the first Monroe H. Martin Prize (1975), which is now awarded by the University of Maryland every five years for a singly authored outstanding applied mathematics research paper. He has published numerous papers and reviews in his fields of expertise, which include elasticity, tensor analysis, scattering theory, and fluid mechanics. (shrink)

We present three natural but distinct formalisations of Einstein’s special principle of relativity, and demonstrate the relationships between them. In particular, we prove that they are logically distinct, but that they can be made equivalent by introducing a small number of additional, intuitively acceptable axioms.

Pointing to the importance of invariance principles has been ranked as one of Einstein’s greatest merits. The symmetries represent an additional category used in a description of the physical world, additional to initial conditions and the very laws of Nature, as distinguished by Newton. Some invariances related to space and time are easy to describe: that the laws of nature are the same everywhere, that they are time independent, and that they do not change if some physical system is subjected (...) to a rotation around an axis in space. The relativistic invariance, which Einstein re-established in his special relativity, was based on giving a full physical meaning to the transformations which Lorentz used to relate observers moving uniformly with respect to each other. He realized that there is no absolute “at rest”, and no sensible “simultaneous” events. What is absolute in his relativity is the constant speed of light, and a well defined proper-time interval. The relativity entered physics as the first great creative principle on Einstein’s list. Subsequently, its marriage to the quantum principle established in atomic physics, brought out the quantum field theory as a mighty tool for the future investigation of the subatomic world. The newly discovered fundamental interactions urged to look for a principle explaining them. It has been found in the form of the gauge principle underlying the present day standard model of elementary particle interactions. It is remarkable that Einstein gave his magical touch also to quantum and gauge principles. Still, the most important Einstein’s idea is that the whole of physics has to be expressed in Minkowski’s space, subject to Lorentz transformations. Today we are aware that, like other symmetries with their restrictions, Lorentz symmetry would be restricted to the non cosmological scale. New ideas in conjunction with the forthcoming cosmological measurements may lead to astonishing results. (shrink)

To what extent are visual fantasies constrained by our perceptual experience of the real world? Our study exploits the fact that people’s knowledge of the appearance of individuals from the early 20th Century derives predominantly from viewing black-and-white media images. An initial experiment shows that mental imagery for individuals from this period are experienced as significantly less colourful than imagery for individuals from the era of colour media. A second experiment manipulated whether participants were instructed to explicitly imagine using colour (...) or not . Results show that colour manipulation only influences imagery for black-and-white era individuals, with no comparable effect on imagery for colour era individuals. This finding is replicated in a third experiment that includes an additional control condition of imagining generic characters . Again, only imagery for black-and-white era individuals is affected by the colour manipulation. Overall these results provide evidence for long-term perceptual specificity effects in mental imagery. We argue that visual fantasies can be constrained by surface features of underlying representations in memory, even when imagining something we have never directly perceived. (shrink)

The use of the material theory of induction to vindicate a scientist's claims of evidential warrant is illustrated with the cases of Einstein's thermodynamic argument for light quanta of 1905 and his recovery of the anomalous motion of Mercury from general relativity in 1915. In a survey of other accounts of inductive inference applied to these examples, I show that, if it is to succeed, each account must presume the same material facts as the material theory and, in (...) class='Hi'>addition, some general principle of inductive inference not invoked by the material theory. Hence these principles are superfluous and the material theory superior in being more parsimonious. (shrink)

No artigo "Einstein y el efecto Compton", publicado neste número de SCIENTIÆ UDIA: , os autores estranham o fato de Einstein não ter declarado mais claramente o quanto esse efeito comprovava definitivamente o carácter corpuscular da radiação. A presente nota crítica pretende fornecer elementos adicionais de apreciação que permitam acompanhar o método de exploração do domínio dos quanta elaborado por Einstein, na ausência de uma teoria adequada, e praticado por ele de 1905 à 1925, evidenciando por esse meio propriedades inéditas (...) e inusuais dos fenômenos quânticos; e também explicitar o alvo que ele queria almejar com sua investigação e entender melhor seu pensamento acerca dos quanta. Três argumentos principais são delineados. (1) O problema dos quanta de luz está estreitamente ligado com aquele das propriedades quânticas da matéria atômica em geral, do qual não pode ser separado. (2) Outro experimento, realizado pouco depois do experimento de Compton, trouxe um elemento adicional, necessário para que se possa atribuir sem nenhuma reticiência uma quantidade de movimento à radiação, isto é, o caráter individual da interação da qual a radiação toma parte. (3) Enfim, os trabalhos de Einstein sobre a estatística quântica, realizados no mesmo período, apontavam na direção da generalização do duplo caráter onda-corpúsculo à radiação, como também à matéria, evidenciando a indiscernibilidade dos estados idênticos e revelando, assim, propriedades fundamentais radicalmente novas que toda teoria quântica futura haveria de incluir. In the article "Einstein y el efecto Compton", published in this issue of SCIENTIÆ UDIA: , the authors wonder why Einstein did not claim unambiguously that this phenomenon was a clear and definitive proof of the corpuscular character of radiation. The aims of the present critical note are to provide additional comments that serve to clarify the method that Einstein used for exploring the quantum domain, in the absence of a satisfactory theory - a method he practiced from 1905 to 1925, and from which he obtained evidence of new and unusual properties of quantum phenomena; and to try to formulate what he wanted to get at in his investigations, so as to understand better his thinking about quanta. Three main arguments are sketched. (1) The problem of light quanta cannot be separated from that of the quantum properties of atomic matter in general. (2) Another experiment, performed shortly after Compton's yielded a further element that was necessary to obtain a definitive answer to the question of whether a quantity of motion can be attributed to radiation. (3) Finally, Einstein's works on quantum statistics during that period pointed towards a generalization of the double wave-corpuscle behavior of radiation, and also of matter, providing evidence for the indistinguishability of identical states, thus revealing radically new fundamental properties that should be accounted for by any further quantum theory. (shrink)

In 1927 at the fifth Solvay Council, that reunited all the aristocracy of theoretical physics, Einstein, regarding with solicitude the new-born “quantum mechanics” of Louis de Broglie, Schrödinger, Heisenberg and Dirac, discerned with his usual sagacity an indelible mark that was destined to become, with time, a subject of passionate discussion among those whose vocation is to adulate this enigmatic and capricious personality.In 1926 Born had given the prophetic stroke to the portrait. Turning to probability as to the official factotum (...) of the reconciliation of the continuous and the discontinuous-here, the associated wave and particle-he transmuted the waves of de Broglie and Schr6dinger into an undulatory calculus o f probabilities, deducing, from a surprising principle, consequences that were even more surprising but always verified through experiment. Parting from the idea that the intensity of the wave is the probability of the detection of the particle at a given point and time, Born replaced the classic principle of addition of partial probabilities with his “principle of the addition of partial amplitudes” that are, as in classical optics, represented by “complex” dimensions, with one real part and one imaginary part. In general, the square of the module of the sum of amplitudes will be the probability. This expression contains, of course, the terms “square” and “rectangular.” The first, if they were alone, would give the former law; as for the second, they express the existence of phenomena of interference that are at the origin of the thousand and one well verified paradoxes of the “new mechanics “-the one thousand and first being the one under consideration here. (shrink)

The use of the material theory of induction to vindicate a scientist’s claims of evidential warrant is illustrated with the cases of Einstein’s thermodynamic argument for light quanta of 1905 and his recovery of the anomalous motion of Mercury from general relativity in 1915. In a survey of other accounts of inductive inference applied to these examples, I show that, if it is to succeed, each account must presume the same material facts as the material theory and, in addition, (...) some general principle of inductive inference not invoked by the material theory. Hence these principles are superfluous and the material theory superior in being more parsimonious. (shrink)

In 1907, Einstein set out to fully relativize all motion, no matter whether uniform or accelerated. After five failed attempts between 1907 and 1918, he finally threw in the towel around 1920, setting himself a new goal. For the rest of his life he searched for a classical field theory unifying gravity and electromagnetism. As he struggled to relativize motion, Einstein had to readjust both his approach and his objectives at almost every step along the way; he got himself hopelessly (...) confused at times; he fooled himself with fallacious arguments and sloppy calculations; and he committed what he later allegedly called the biggest blunder of his career: he introduced the cosmological constant. There is a very uplifting moral to this somber tale. Although Einstein never reached his original destination, the harvest of his thirteen-year odyssey is quite impressive. First of all, what is left of absolute motion in general relativity is far more palatable than absolute motion in special relativity or Newtonian theory. And general relativity does seem to eliminate absolute space. More importantly, from a modern physics point of view, Einstein produced a spectacular new theory of gravity based on what he called the equivalence principle. This principle says that inertial and gravitational effects are due to one and the same structure, the inertio-gravitational field, which in Einstein’s theory is represented by a metric tensor field. In addition to laying the foundations of this theory, Einstein, among other things, launched relativistic cosmology, suggested the possibility of gravitational waves, gave the first sensible definition of a space-time singularity, and caught on to the intimate connection between general covariance and energy-momentum conservation, an example of the general connection between symmetries and conservation laws of Noether’s theorems. These results more than make up for the—at least by the standards of modern philosophy of science—rather opportunistic way in which they were obtained.. (shrink)

In a recent paper, I have analysed and criticised Leggett and Garg’s argument to the effect that macroscopic realism contradicts quantum mechanics, by contrasting their assumptions to the example of Bell’s stochastic pilot-wave theories, and have applied Dzhafarov and Kujala’s analysis of contextuality in the presence of signalling to the case of the Leggett–Garg inequalities. In this chapter, I discuss more in general the motivations for macroscopic realism, taking a cue from Einstein’s criticism of the Bohm theory, then go on (...) to summarise my previous results, with a few additional comments on other recent work on Leggett and Garg. [To appear in: E. Dzhafarov, Contextuality from Quantum Physics to Psychology.]. (shrink)

En la primera parte de este artículo, respondemos a los comentarios críticos de Michel Paty sobre nuestro trabajo "Einstein y el efecto Compton". Si bien nuestra intención no fue evaluar la respuesta de Einstein a la evidencia experimental de la hipótesis cuántica de la luz más allá del año 1923, en la segunda parte del artículo evaluamos dos importantes experimentos completados en 1924: los realizados por Bothe y Geiger en Alemania y los de Compton y Simon en los Estados Unidos. (...) Discutimos por qué ambos experimentos proporcionaron pruebas adicionales que respaldaron los puntos de vista de Einstein sobre la teoría cuántica de la radiación. Sin embargo, afirmamos que aun después de conocer estos resultados, Einstein nunca expresó un juicio categórico sobre la realidad de los cuantos de luz tal como el que formuló De Broglie a principios de 1923, con el que comparamos el punto de vista de Einstein. In the first part of this paper we reply to Michel Paty's critical remarks on our paper "Einstein and the Compton effect". We state that we did not evaluate Einstein's response to the experimental evidence about the light quantum hypothesis beyond 1923. Nevertheless, in the second part we analyze two important experiments completed in 1924: those performed by Bothe and Geiger in Germany and by Compton and Simon in the United States. We point out that both experiments provided additional evidence that supported Einstein's views about the quantum theory of radiation. Nonetheless, we contend that even after becoming aware of these results, Einstein never expressed a categorical judgment about the reality of light quanta, such as the one stated by De Broglie as early as 1923, with which we compared Einstein's position. (shrink)

This book presents the first English translation of the original French treatise “La Physique d’Einstein” written by the young Georges Lemaître in 1922, only six years after the publication of Albert Einstein’s theory of General Relativity. It includes an historical introduction and a critical edition of the original treatise in French supplemented by the author’s own later additions and corrections. -/- Monsignor Georges Lemaître can be considered the founder of the “Big Bang Theory” and a visionary architect of modern Cosmology. (...) The scientific community is only beginning to grasp the full extent of the legacy of this towering figure of 20th century physics. Against the best advice of the greatest names of his time, the young Lemaître was convinced, solely through the study of Einstein’s theory of General Relativity, that space and time must have had a beginning with a tremendous “Big Bang” from a “quantum primeval atom” resulting in an ever-expanding Universe with a positive cosmological constant. -/- But how did the young Lemaître, essentially on his own, come to grips with the physics of Einstein? A year before his ordination as a diocesan priest, he submitted the audacious treatise, published in this book, that was to earn him Fellowships to study at Cambridge, MIT and Harvard, and launched him on a scientific path of ground-breaking discoveries. Almost a century after Lemaître’s seminal publications of 1927 and 1931, this highly pedagogical treatise is still of timely interest to young minds and remains of great value from a history of science perspective. (shrink)

The relationship between Albert Einstein’s special theory of relativity and Hendrik A. Lorentz’s ether theory is best understood in terms of competing interpretations of Lorentz invariance. In the 1890s, Lorentz proved and exploited the Lorentz invariance of Maxwell’s equations, the laws governing electromagnetic fields in the ether, with what he called the theorem of corresponding states. To account for the negative results of attempts to detect the earth’s motion through the ether, Lorentz, in effect, had to assume that the laws (...) governing the matter interacting with the fields are Lorentz invariant as well. This additional assumption can be seen as a generalization of the well-known contraction hypothesis. In Lorentz’s theory, it remained an unexplained coincidence that both the laws governing fields and the laws governing matter should be Lorentz invariant. In special relativity, by contrast, the Lorentz invariance of all physical laws directly reflects the Minkowski space-time structure posited by the theory. One can use this observation to produce a common-cause argument to show that the relativistic interpretation of Lorentz invariance is preferable to Lorentz’s interpretation. (shrink)

The present authors have given a mathematical model of Mach's principle and of the Mach–Einstein doctrine about the complete induction of the inertial masses by the gravitation of the universe. The analytical formulation of the Mach–Einstein doctrine is based on Riemann's generalization of the Lagrangian analytical mechanics (with a generalization of the Galilean transformation) on Mach's definition of the inertial mass and on Einstein's principle of equivalence. All local and cosmological effects—which are postulated as consequences of Mach's principle by (...) C. Neumann, Mach, Friedländer and Einstein—result from the Riemannian dynamics with the Mach–Einstein doctrine. In celestial mechanics it follows, in addition, Einstein's formula for the perihelion motion. In cosmology, the Riemannian mechanics yields two models of an evolutionary universe with the expansion lows R ~ t or R ~ t2. In this paper, secular consequences of the Mach–Einstein doctrine are examined concerning palaeogeophysics and celestial mechanics. The research predicted secular decrease of the Earth's flattening and secular acceleration of the motion of the Moon and of the planets. The numerical values of this secular effect agree very well with the empirical facts. In all cases, the secular variation $\dot{\alpha}$ of the parameter α is the order of magnitude $\dot{\alpha}=-H_0 \alpha$ , where H0 is the instantaneous value of the Hubble constant: $H_0 =\left({\dot{R}/R} \right)_0 \approx \left( {0.5-1.0} \right) \times 10^{-10}a^{-1}$ . The relation of the secular consequences of the Mach–Einstein doctrine to those of Dirac's hypothesis on the expanding Earth, and to Darwin's theory of tidal friction are also discussed. (shrink)

Einstein wrote his famous sentence "God does not play dice with the universe" in a letter to Max Born in 1920. All experiments have confirmed that quantum mechanics is neither wrong nor “incomplete”. One can says that God does play dice with the universe. Let quantum mechanics be granted as the rules generalizing all results of playing some imaginary God’s dice. If that is the case, one can ask how God’s dice should look like. God’s dice turns out to be (...) a qubit and thus having the shape of a unit ball. Any item in the universe as well the universe itself is both infinitely many rolls and a single roll of that dice for it has infinitely many “sides”. Thus both the smooth motion of classical physics and the discrete motion introduced in addition by quantum mechanics can be described uniformly correspondingly as an infinite series converges to some limit and as a quantum jump directly into that limit. The second, imaginary dimension of God’s dice corresponds to energy, i.e. to the velocity of information change between two probabilities in both series and jump. (shrink)

After some considerations about the equivalence of the objective local theories to the deterministic theories of Bell's type, a simple and systematic way to deduce inequalities from Einstein locality is introduced: All the inequalities deduced by Bell and by other authors, as well as several new ones, are so obtained. Some theorems are proven which show how striking the difference is at small angles between a correlation function satisfying Einstein locality and the quantum mechanical one. Experiments at small angles involve (...) weaker additional assumptions than those used up to now in experimental research on Bell's inequality. (shrink)

The success of a few theories in statistical thermodynamics can be correlated with their selectivity to reality. These are the theories of Boltzmann, Gibbs, and Einstein. The starting point is Carnot’s theory, which defines implicitly the general selection of reality relevant to thermodynamics. The three other theories share this selection, but specify it further in detail. Each of them separates a few main aspects within the scope of the implicit thermodynamic reality. Their success grounds on that selection. Those aspects can (...) be represented by corresponding oppositions. These are: macroscopic – microscopic; elements – states; relational – non-relational; and observable – theoretical. They can be interpreted as axes of independent qualities constituting a common qualitative reference frame shared by those theories. Each of them can be situated in this reference frame occupying a different place. This reference frame can be interpreted as an additional selection of reality within Carnot’s initial selection describable as macroscopic and both observable and theoretical. The deduced reference frame refers implicitly to many scientific theories independent of their subject therefore defining a general and common space or subspace for scientific theories (not for all). The immediate conclusion is: The examples of a few statistical thermodynamic theories demonstrate that the concept of “reality” is changed or generalized, or even exemplified (i.e. “de-generalized”) from a theory to another. Still a few more general suggestions referring the scientific realism debate can be added: One can admit that reality in scientific theories is some partially shared common qualitative space or subspace describable by relevant oppositions and rather independent of their subject quite different in general. Many or maybe all theories can be situated in that space of reality, which should develop adding new dimensions in it for still newer and newer theories. Its division of independent subspaces can represent the many-realities conception. The subject of a theory determines some relevant subspace of reality. This represents a selection within reality, relevant to the theory in question. The success of that theory correlates essentially with the selection within reality, relevant to its subject. (shrink)

This paper analyzes correspondence between Reichenbach and Einstein from the spring of 1926, concerning what it means to ‘geometrize’ a physical field. The content of a typewritten note that Reichenbach sent to Einstein on that occasion is reconstructed, showing that it was an early version of §49 of the untranslated Appendix to his Philosophie der Raum-Zeit-Lehre, on which Reichenbach was working at the time. This paper claims that the toy-geometrization of the electromagnetic field that Reichenbach presented in his note should (...) not be regarded as merely a virtuoso mathematical exercise, but as an additional argument supporting the core philosophical message of his 1928 monograph. This paper concludes by suggesting that Reichenbach’s infamous ‘relativization of geometry’ was only a stepping stone on the way to his main concern—the question of the ‘geometrization of gravitation’. (shrink)

Albert Einstein's Quest as a Scientist and as a Jew to Replace a Forsaken God.

A new form of the Hyperbolic Pythagorean Theorem, which has a striking intuitive appeal and offers a strong contrast to its standard form, is presented. It expresses the square of the hyperbolic length of the hypotenuse of a hyperbolic right-angled triangle as the “Einstein sum” of the squares of the hyperbolic lengths of the other two sides, Fig. 1, thus completing the long path from Pythagoras to Einstein. Following the pioneering work of Varičak it is well known that relativistic velocities (...) are governed by hyperbolic geometry in the same way that prerelativistic velocities are governed by Euclidean geometry. Unlike prerelativistic velocity composition, given by the ordinary vector addition, the composition of relativistic velocities, given by the Einstein addition, is neither commutative nor associative due to the presence of Thomas precession. Following the discovery of the mathematical regularity that Thomas precession stores, it is now possible to extend Thomas precession by abstraction, (i) allowing hyperbolic geometry to be studied by means of analogies that it shares with Euclidean geometry; and, similarly (ii) allowing velocities and accelerations in relativistic mechanics to be studied by means of analogies that they share with velocities and accelerations in classical mechanics. The abstract Thomas precession, called the Thomas gyration, gives rise to gyrovector space theory in which the prefix gyro is used extensively in terms like gyrogroups and gyrovector spaces, gyroassociative and gyrocommutative laws, gyroautomorphisms, gyrotranslations, etc. We demonstrate the superiority of our gyrovector space formalism in capturing analogies by deriving the Hyperbolic Pythagorean Theorem in a form fully analogous to its Euclidean counterpart, thus contrasting it with the standard form in which the Hyperbolic Pythagorean Theorem is known in the literature. The hyperbolic metric, which supports the Hyperbolic Pythagorean Theorem, has a dual metric. We show that the dual metric does not support a Pythagorean theorem but, instead, it supports the π-Theorem according to which the sum of the three dual angles of a hyperbolic triangle is π. (shrink)

We formulate a model of EPR experiments by including variables determining whether a photon will be detected or not. The resulting deterministic model satisfies Bell's original inequality even though it can agree exactly with the quantum mechanical predictions for the performed experiments. It violates variations of the inequality used in the interpretation of the experiments and deduced with the help of additional assumptions.

Gyrogroup theory [A. A. Ungar, Found. Phys. 27, 881–951 (1997)] enables the study of the algebra of Einstein's addition to be guided by analogies shared with the algebra of vector addition. The capability of gyrogroup theory to capture analogies is demonstrated in this article by exposing the relativistic composite-velocity reciprocity principle. The breakdown of commutativity in the Einstein velocity addition ⊕ of relativistically admissible velocities seemingly gives rise to a corresponding breakdown of the relativistic composite-velocity reciprocity (...) principle, since seemingly (i) on one hand, the velocity reciprocal to the composite velocity u⊕v is −(u⊕v) and (ii) on the other hand, it is (−v)⊕(−u). But (iii) −(u⊕v)≠(−v)⊕(−u). We remove the confusion in (i), (ii), and (iii) by employing the gyrocommutative gyrogroup structure of Einstein's addition and, subsequently, present the relativistic composite-velocity reciprocity principle with the Thomas rotation that it involves. (shrink)

The foundations of Wesson’s induced matter theory are analyzed. It is shown that the empty—without matter—5-dimensional bulk must be regarded as a Weylian space rather than as a Riemannian one. Revising the geometry of the bulk, we have assumed that a Weylian connection vector and a gauge function exist in addition to the metric tensor. The framework of a Weyl–Dirac version of Wesson’s theory is elaborated and discussed. In the 4-dimensional hypersurface (brane), one obtains equations describing both fields, the (...) gravitational and the electromagnetic. The result is a geometrically based unified theory of gravitation and electromagnetism with mass and current induced by the bulk. In special cases on obtains on the brane the equations of Einstein–Maxwell, or these of the original induced matter theory. (shrink)

ABSTRACT. May scientists rely on substantive, a priori presuppositions? Quinean naturalists say "no," but Michael Friedman and others claim that such a view cannot be squared with the actual history of science. To make his case, Friedman offers Newton's universal law of gravitation and Einstein's theory of relativity as examples of admired theories that both employ presuppositions (usually of a mathematical nature), presuppositions that do not face empirical evidence directly. In fact, Friedman claims that the use of such presuppositions (...) is a hallmark of "science as we know it." But what should we say about the special sciences, which typically do not rely on the abstruse formalisms one finds in the exact sciences? I identify a type of a priori presupposition that plays an especially striking role in the development of empirical psychology. These are ontological presuppositions about the type of object a given science purports to study. I show how such presuppositions can be both a priori and rational by investigating their role in an early flap over psychology's contested status as a natural science. The flap focused on one of the field's earliest textbooks, William James's Principles of Psychology. The work was attacked precisely for its reliance on a priori presuppositions about what James had called the "mental state," psychology's (alleged) proper object. I argue that the specific presuppositions James packed into his definition of the "mental state" were not directly responsible to empirical evidence, and so in that sense were a priori; but the presuppositions were rational in that they were crafted to help overcome philosophical objections (championed by neo-Hegelians) to the very idea that there can be a genuine science of mind. Thus, my case study gives an example of substantive, a priori presuppositions being put to use—to rational use—in the special sciences. In addition to evaluating James's use of presuppositions, my paper also offers historical reflections on two different strands of pragmatist philosophy of science. One strand, tracing back through Quine to C. S. Peirce, is more naturalistic, eschewing the use of a priori elements in science. The other strand, tracing back through Kuhn and C. I. Lewis to James, is more friendly to such presuppositions, and to that extent bears affinity with the positivist tradition Friedman occupies. (shrink)

Most of the nearly innumerable attempts to provide for a sound understanding of the gedanken experiment of Einstein, Podolsky, and Rosen (EPR) contain additional ideas, notions or features imposed on pioneer or traditional quantum mechanics (TQM). In the present paper the problem is analyzed without employing any new or philosophically contested concept. We do even without referring to the probability calculus, and we especially avoid any admixture of realistic ideas. Neither entanglement nor special features of “states” are used. Instead, formulating (...) strictly within the framework of TQM and using an ensemble approach, the crucial point is boiled down to the decision between separability and non-separability. The corresponding second-order correlation functions Δs and Δn−s, resp., which predict the experimental outcome, may differ by a factor of 2 if certain operator pairs are maximally non-commuting. Even in the case of commuting pairs, an experimentally relevant difference between the Δ-functions might exist. Taking into account the experimental evidence, it is unavoidable to accept that the sub-ensembles involved in EPR-type experiments are in fact non-separable. This result has been obtained without resort to Bell's inequality. (shrink)

Einstein’s razor, a corollary of Ockham’s razor, is often paraphrased as follows: make everything as simple as possible, but not simpler. This rule of thumb describes the challenge that designers of a legal system face—to craft simple laws that produce desired ends, but not to pursue simplicity so far as to undermine those ends. Complexity, simplicity’s inverse, taxes cognition and increases the likelihood of suboptimal decisions. In addition, unnecessary legal complexity can drive a misallocation of human capital toward comprehending (...) and complying with legal rules and away from other productive ends. While many scholars have offered descriptive accounts or theoretical models of legal complexity, most empirical research to date has been limited to simple measures of size, such as the number of pages in a bill. No extant research rigorously applies a meaningful model to real data. As a consequence, we have no reliable means to determine whether a new bill, regulation, order, or precedent substantially effects legal complexity. In this paper, we begin to address this need by developing a proposed empirical framework for measuring relative legal complexity. This framework is based on “knowledge acquisition”, an approach at the intersection of psychology and computer science, which can take into account the structure, language, and interdependence of law. We then demonstrate the descriptive value of this framework by applying it to the U.S. Code’s Titles, scoring and ranking them by their relative complexity. We measure various features of a title including its structural size, the net flow of its intra-title citations and its linguistic entropy. Our framework is flexible, intuitive, and transparent, and we offer this approach as a first step in developing a practical methodology for assessing legal complexity. (shrink)

This chapter looks at six arguments against Tensism. They are, equivalently, arguments for Anti‐Tensism. The arguments are of three basic kinds: those that argue that Tensism is incoherent or mysterious, those that argue that it is in irresolvable conflict with modern science, and those that fault Tensism for its unexplainable or brute necessities. The chapter considers the objection that Tensism cannot sensibly account for the rate of the flow of time. It shows in which a variety of objections based on (...) Truthmaker Theory are lodged against various versions of Tensism. The chapter looks at science, especially Einstein's theory of relativity, as the basis for an argument against Tensism. It concerns additional philosophical objections to Tensism and then considers epistemological problems for Tensism; and McTaggart's argument that Tensism is self‐contradictory. The chapter explores the number of brute necessities for which Tensism can provide no simple explanation. (shrink)

After 1905, physics would never be the same. In those 12 months, Einstein shattered many cherished scientific beliefs with five great papers that would establish him as the world's leading physicist. On their 100th anniversary, this book brings those papers together in an accessible format.

The photon box thought experiment can be considered a forerunner of the EPR-experiment: by performing suitable measurements on the box it is possible to ``prepare'' the photon, long after it has escaped, in either of two complementary states. Consistency requires that the corresponding box measurements be complementary as well. At first sight it seems, however, that these measurements can be jointly performed with arbitrary precision: they pertain to different systems (the center of mass of the box and an internal clock, (...) respectively). But this is deceptive. As we show by explicit calculation, although the relevant quantities are simultaneously measurable, they develop non-vanishing commutators when calculated back to the time of escape of the photon. This justifies Bohr's qualitative arguments in a precise way; and it illustrates how the details of the dynamics conspire to guarantee the requirements of complementarity. In addition, our calculations exhibit a ``fine structure'' in the distribution of the uncertainties over the complementary quantities: depending on when the box measurement is performed, the resulting quantum description of the photon differs. This brings us close to the argumentation of the later EPR thought experiment. (shrink)

Bohr’s reply to Einstein, Podolsky, and Rosen’s argument for the incompleteness of quantum theory is notoriously difficult to unravel. It is so diffcult, in fact, that over 60 years later, there remains important work to be done understanding it. Work by Fine , Beller and Fine , and Beller goes a long way towards correcting earlier misunderstandings of Bohr’s reply. This essay is intended as a contribution to the program of getting to the truth of the matter, both historically and (...) philosophically. In a paper of this length, a full account of Bohr’s reply is impossible, and so I shall focus on one issue where it seems further clarification is required, namely, Bohr’s attempt to illustrate EPR’s argument by means of a thought experiment. In addition, I shall attempt to clarify a few other points which, however minor, have apparently contributed to misunderstandings of Bohr’s position. As the title of this paper suggests, an account of these few points does not constitute an account of Bohr’s reply, but it is an important step in that direction. (shrink)

In 1922, Albert Einstein rejected Bergson’s concept of time. He even declared that Bergson’s duration did not exist, something that Bergson never quite came to terms with. On the other hand, some of Bergson’s reflections indicated that in a certain respect he was close to the spirit of modern physics, especially quantum theory. The author, therefore, asks whether it is possible to equate Bergson’s duration with the quantum space-time continuum and thus rehabilitate Bergson’s concept. The first part of the article, (...) in addition to the definition of duration, focuses on the connection of the subject, time, and matter in Bergson, which represents one of the points of contact with quantum theory. The second part describes the role of the subject in quantum theory. The third part presents the definition of the mentioned space-time continuum. The final section compares the two concepts and answers the research question. (shrink)

Cornelius Lanczos is professor emeritus at the Dublin Institute for Advanced Studies. Hungarian-born he made significant contributions to the development of relativity and quantum theory in the earlier decades of this century, and during the past twenty years he has established himself as an authority on numerical analysis. In addition he has a deep appreciation of literature from the Old Testament onwards, of music and of the arts. His writings in recent years have consisted largely in philosophical speculations on (...) aspects of physics. The present book is an historical account of man’s investigation of the nature and properties of space. Lanczos’ gift of clear exposition and his broad culture have made it a readable and valuable review of the development of the notion of space throughout the ages. (shrink)

Albert Einstein insists that his epistemology made his discovery of relativity possible. He believed it was his understanding of the relationship of experience and reason that allowed him to reconsider certain “truths” of physics. Specifically, he believed that reality and thought were independent but related, and that conceptual systems are independent of but conditioned by experience. Failure to understand the relation between experience and reason had, Einstein believed, limited progress in science. His understanding of the relation, on the other hand, (...) enabled him to formulate relativity theory and therefore provides one example of the relevance of philosophy to scientific inquiry. When Albert Einstein discussed his discoveries in physics, particularly the theory of relativity, he often began with an explanation of his epistemology and referred to thinkers like Hume and Kant. Einstein may have been a physicist, but he had definite ideas about how we know and regarded epistemological theories as crucial to science, especially to physics. Indeed, he placed such importance on the question of how we know that the discussion of his work in his “Autobiographical Notes” begins with the question, “What, precisely, is ‘thinking?'” (1951, 7). The correct answer to this philosophical question, he believed, makes progress in science possible. The present article focuses on the relationship of the two elements, experience and reason, in Einstein's epistemology. Einstein himself frequently concentrates on what he characterizes as “the eternal antithesis between the two inseparable components of our knowledge, the empirical and the rational” (1934b, 271) in his papers and lectures on physics, for he regards them as independent in origin but related in scientific truth. His insistence that experience and reason do not determine one another yet must be related proved, for him, to be a necessary but not sufficient condition for the formulation of relativity theory and for scientific progress in general. The discussion of the relationship has four parts. First, experience and reason are explained; included in this explanation are Einstein's reasons for maintaining that the two are independent. The second section discusses the connection between the two that produces truth and knowledge. The third section follows with discussion of the way that Einstein believes reason can be both conditioned by and independent of experience. Finally, the significance of this understanding of the relation for relativity theory is examined. (shrink)

Some implications of Tomasello et al.'s theory derive from incorporating a variant of a common assumption that humans are biologically adapted to take an intentional stance in relation to conspecifics. I argue that, rather than being cued, intentions and other dispositional states may be inferred logically from an evolved commitment to determinism and evidence of state-dependent behavior.

In a 1936 manuscript submitted to the Physical Review, Albert Einstein and Nathan Rosen famously claimed that gravitational waves do not exist. It has generally been assumed that there was a conceptual error underlying this fallacious claim. It will be shown, through a detailed study of the extant referee report, that this claim was probably only the result of a calculational error, the accidental use of a pathological coordinate transformation.

Einstein, in his “Zur Elektrodynamik bewegter Körper”, gave a physical (operational) meaning to “time” of a remote event in describing “motion” by introducing the concept of “synchronous stationary clocks located at different places”. But with regard to “place” in describing motion, he assumed without analysis the concept of a system of co-ordinates.In the present paper, we propose a way of giving physical (operational) meaning to the concepts of “place” and “co-ordinate system”, and show how the observer can define both the (...) place and time of a remote event. Following Einstein, we consider another system “in uniform motion of translation relatively to the former”. Without assuming “the properties of homogeneity which we attribute to space and time”, we show that the definitions of space and time in the two systems are linearly related. We deduce some novel consequences of our approach regarding faster-than-light observers and particles, “one-way” and “two-way” velocities of light, symmetry, the “group property” of inertial reference frames, length contraction and time dilatation, and the “twin paradox”. Finally, we point out a flaw in Einstein’s argument in the “Electrodynamical Part” of his paper and show that the Lorentz force formula and Einstein’s formula for transformation of field quantities are mutually consistent. We show that for faster-than-light bodies, a simple modification of Planck’s formula for mass suffices. (Except for the reference to Planck’s formula, we restrict ourselves to Physics of 1905.). (shrink)

Quantum mechanics notoriously faces the measurement problem, the problem that if read thoroughly, it implies the nonexistence of definite outcomes in measurement procedures. A plausible reaction to this and to related problems is to regard a system's quantum state |ψ> merely as an indication of our lack of knowledge about the system, i.e., to interpret it epistemically. However, there are radically different ways to spell out such an epistemic view of the quantum state. We here investigate recent developments in the (...) branch that introduces hidden variables λ in addition to the quantum state |ψ> and has its roots in Einstein's views. In particular, we confront purported achievements of a concrete model that has been considered to serve as evidence for an epistemic view of the envisioned kind, as well as specific no-go results and their import. It will be argued that while an epistemic account of the particular kind is not straightforwardly ruled out by the no-go results, they demonstrate that the evidential character of the model(s) discussed rests on a rather shaky foundation, and that they make some achievements widely recognized in the literature appear worthy of doubt. (shrink)

This concise book introduces nonphysicists to the core philosophical issues surrounding the nature and structure of space and time, and is also an ideal resource for physicists interested in the conceptual foundations of space-time theory. Tim Maudlin's broad historical overview examines Aristotelian and Newtonian accounts of space and time, and traces how Galileo's conceptions of relativity and space-time led to Einstein's special and general theories of relativity. Maudlin explains special relativity using a geometrical approach, emphasizing intrinsic space-time structure rather (...) than coordinate systems or reference frames. He gives readers enough detail about special relativity to solve concrete physical problems while presenting general relativity in a more qualitative way, with an informative discussion of the geometrization of gravity, the bending of light, and black holes. Additional topics include the Twins Paradox, the physical aspects of the Lorentz-FitzGerald contraction, the constancy of the speed of light, time travel, the direction of time, and more.Introduces nonphysicists to the philosophical foundations of space-time theory Provides a broad historical overview, from Aristotle to Einstein Explains special relativity geometrically, emphasizing the intrinsic structure of space-time Covers the Twins Paradox, Galilean relativity, time travel, and more Requires only basic algebra and no formal knowledge of physics. (shrink)

This paper discusses some philosophical aspects related to the recent publication of the experimental results of the 2017 black hole experiment, namely the first image of the supermassive black hole at the center of galaxy M87. In this paper I present a philosophical analysis of the 2017 Event Horizon Telescope (EHT) black hole experiment. I first present Hacking’s philosophy of experimentation. Hacking gives his taxonomy of elements of laboratory science and distinguishes a list of elements. I show that the EHT (...) experiment conforms to major elements from Hacking’s list. I then describe with the help of Galison’s Philosophy of the Shadow how the EHT Collaboration created the famous black hole image. Galison outlines three stages for the reconstruction of the black hole image: Socio-Epistemology, Mechanical Objectivity, after which there is an additional SocioEpistemology stage. I subsequently present my own interpretation of the reconstruction of the black hole image and I discuss model fitting to data. I suggest that the main method used by the EHT Collaboration to assure trust in the results of the EHT experiment is what philosophers call the Argument from Coincidence. I show that using this method for the above purpose is problematic. I present two versions of the Argument from Coincidence: Hacking’s Coincidence and Cartwright’s Reproducibility by which I analyse the EHT experiment. The same estimation of the mass of the black hole is reproduced in four different procedures. The EHT Collaboration concludes: the value we have converged upon is robust. I analyse the mass measurements of the black hole with the help of Cartwright’s notion of robustness. I show that the EHT Collaboration construe Coincidence/Reproducibility as Technological Agnosticism and I contrast this interpretation with van Fraassen’s scientific agnosticism. (shrink)